On the Humble Origins of the Brownian Entropic Force

TL;DR

This paper rigorously derives the Brownian entropic force from classical thermodynamics, clarifying its kinetic origin and highlighting its significance in various physical and computational models.

Contribution

It provides the first rigorous derivation of the Brownian entropic force using the Gibbs canonical partition function, connecting it to kinetic theory.

Findings

Derivation of the Brownian entropic force from thermodynamic principles

Demonstration of the kinetic origin of the entropic force

Implications for molecular dynamics and particle physics models

Abstract

Recognition that certain forces arising from the averaging of the multiple impacts of a solute particle by the surrounding solvent particles undergoing random thermal motion can be of an entropic nature has led to the incorporation of these forces and their related entropies into theoretical protocols ranging from molecular-dynamics simulations to the modeling of quarkonium suppression in particle physics. Here we present a rigorous derivation of this Brownian entropic force by means of the classical Gibbs canonical partition function and in so doing provide a heuristic demonstration of its kinetic origin.